Operator formalism and free field representation for minimal models on Riemann surfaces

1990 ◽  
Vol 338 (2) ◽  
pp. 415-441 ◽  
Author(s):  
M. Frau ◽  
A. Lerda ◽  
J.G. McCarthy ◽  
S. Sciuto
Keyword(s):  
Riemann Surfaces ◽  
Free Field ◽  
Minimal Models ◽  
Operator Formalism ◽  
Field Representation

scholarly journals Free field representation for WZNW models on Riemann surfaces

1990 ◽  
Vol 245 (3-4) ◽  
pp. 453-464 ◽  
Author(s):  
M. Frau ◽  
A. Lerda ◽  
J.G. McCarthy ◽  
S. Sciuto ◽  
J. Sidenius
Keyword(s):  
Riemann Surfaces ◽  
Free Field ◽  
Field Representation

MODULAR INVARIANT ONE-POINT CORRELATION FUNCTIONS FOR SU(2) WESS-ZUMINO MODEL

1992 ◽  
Vol 07 (25) ◽  
pp. 6257-6272 ◽  
Author(s):  
O.D. ANDREEV
Keyword(s):  
Correlation Functions ◽  
Riemann Surfaces ◽  
Free Field ◽  
Necessary Condition ◽  
Modular Invariant ◽  
Field Representation ◽  
Conformal Field ◽  
Higher Genus ◽  
Point Correlation ◽  
Zumino Model

We calculate one-point correlation functions of SU(2) Wess-Zumino model (WZM) on a torus using the Wakimoto free field representation. Their modular invariance is proved. It is a necessary condition of extending the WZ conformal field theory to higher genus Riemann surfaces.

WESS-ZUMINO-WITTEN MODEL AS A THEORY OF FREE FIELDS

1990 ◽  
Vol 05 (13) ◽  
pp. 2495-2589 ◽  
Author(s):  
A. GERASIMOV ◽  
A. MOROZOV ◽  
M. OLSHANETSKY ◽  
A. MARSHAKOV ◽  
S. SHATASHVILI
Keyword(s):  
Riemann Surfaces ◽  
Central Charge ◽  
Free Field ◽  
Heisenberg Algebra ◽  
Momentum Tensor ◽  
Point Of View ◽  
Special Role ◽  
Field Representation ◽  
Conformal Blocks ◽  
Free Fields

The free field representation or "bosonization" rule1 for Wess-Zumino-Witten model (WZWM) with arbitrary Kac-Moody algebra and arbitrary central charge is discussed. Energy-momentum tensor, arising from Sugawara construction, is quadratic in the fields. In this way, all known formulae for conformal blocks and correlators may be easily reproduced as certain linear combinations of correlators of these free fields. Generalization to conformal blocks on arbitrary Riemann surfaces is straightforward. However, projection rules in the spirit of Ref. 2 are not specified. The special role of βγ systems is emphasized. From the mathematical point of view, the construction involved represents generators of Kac-Moody (KM) algebra in terms of generators of a Heisenberg one. If WZW Lagrangian is considered as d−1 of Kirillov form on an orbit of KM algebra,3 then the free fields of interest (i.e. generators of the Heisenberg algebra) diagonalize Kirillov form and the action. Reduction of KM algebra within the same construction should naturally lead to arbitrary coset models.

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

Tadpole operator for minimal models on arbitrary genus Riemann surfaces

1990 ◽  
Vol 237 (3-4) ◽  
pp. 379-385 ◽  
Author(s):  
G. Cristofano ◽  
G. Maiella ◽  
R. Musto ◽  
F. Nicodemi
Keyword(s):  
Riemann Surfaces ◽  
Minimal Models ◽  
Arbitrary Genus

BRST COHOMOLOGY IN QUANTUM AFFINE ALGEBRA $U_q \left( {\widehat{sl_2 }} \right)$

1994 ◽  
Vol 09 (14) ◽  
pp. 1253-1265 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Free Field ◽  
Classical Case ◽  
Explicit Construction ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Field Representation ◽  
Highest Weight ◽  
Brst Charge ◽  
Brst Cohomology ◽  
Highest Weight Representation

Using free field representation of quantum affine algebra [Formula: see text], we investigate the structure of the Fock modules over [Formula: see text]. The analysis is based on a q-analog of the BRST formalism given by Bernard and Felder in the affine Kac-Moody algebra [Formula: see text]. We give an explicit construction of the singular vectors using the BRST charge. By the same cohomology analysis as the classical case (q=1), we obtain the irreducible highest weight representation space as a non-trivial cohomology group. This enables us to calculate a trace of the q-vertex operators over this space.

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